Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 9, No 4, (2006), 333p-349p
In this paper, a space fractional diffusion equation (SFDE) with nonhomogeneous
boundary conditions on a bounded domain is considered. A
new matrix transfer technique (MTT) for solving the SFDE is proposed.
The method is based on a matrix representation of the fractional-in-space
operator and the novelty of this approach is that a standard discretisation
of the operator leads to a system of linear ODEs with the matrix raised
to the same fractional power. Analytic solutions of the SFDE are derived.
Finally, some numerical results are given to demonstrate that the MTT is
a computationally efficient and accurate method for solving SFDE.